Here is the full list of all 5 Call of Duty: Black Ops II Multiplayer achievements.
Win 5 multiplayer League Play games after being placed in a division.
Win 10 multiplayer games while playing in Combat Training playlists.
Win 10 multiplayer games while playing in Party Games playlists.
Prestige once in multiplayer Public Match.
Reach Sergeant (Level 10) in multiplayer Public Match.